Problem: Solve for $q$. Reduce any fractions to lowest terms. Don't round your answer, and don't use mixed fractions. $22q+73 > 52q + 63$
Answer: $\begin{aligned}22q+73 & > 52q + 63 \\\\ 22q&> 52q-10 &(\text{Subtract } 73 \text{ from both sides}) \\\\ -30q &> -10 &(\text{Subtract } 52q \text{ from both sides})\\\\ 30q&< 10&(\text{Multiply both sides by }-1)\\\\ q&<\dfrac{1}{3}&(\text{Divide both sides by }30 \text{ and simplify}) \end{aligned}$ [Why did the inequality sign flip when we multiplied by -1?] In conclusion, the answer is $q < \dfrac{1}{3}$.